What is the integral from 0 to 1/2 of 3x-6x^2 ?

The integral from 0 to 1/2 of 3x-6x^2 is 1/8

integral from 0 to 1/2 of 3x-6x^2

\int_{0}^{\frac{1}{2}} 3 x - 6 x^{2} d x

\frac{1}{8}

Decimal

0.125

Solution steps

\int_{0}^{\frac{1}{2}} 3 x - 6 x^{2} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{\frac{1}{2}} 3 x d x - \int_{0}^{\frac{1}{2}} 6 x^{2} d x

\int_{0}^{\frac{1}{2}} 3 x d x = \frac{3}{8}

\int_{0}^{\frac{1}{2}} 6 x^{2} d x = \frac{1}{4}

= \frac{3}{8} - \frac{1}{4}

Simplify

\frac{3}{8} - \frac{1}{4} : \frac{1}{8}

= \frac{1}{8}

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What is the integral from 0 to 1/2 of 3x-6x^2 ?
The integral from 0 to 1/2 of 3x-6x^2 is 1/8